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Title: Standard Deviation
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Series: Probability Theory
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Chapter: Random Variables
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YouTube-Title: Probability Theory 17 | Standard Deviation
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Bright video: Watch on YouTube
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Dark video: Watch on YouTube
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Ad-free video: Watch Vimeo video
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Original video for YT-Members (bright): Watch on YouTube
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Original video for YT-Members (dark): Watch on YouTube
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Exercise Download PDF sheets
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: pt17_sub_eng.srt missing
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Download bright video: Link on Vimeo
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Download dark video: Link on Vimeo
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Definitions in the video: standard deviation
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Let $(\Omega, \mathcal{A}, \mathbb{P})$ be a probability space and $X \colon \Omega \rightarrow \mathbb{R}$ be a random variable. What is never correct for the standard deviation $\sigma(X)$?
A1: $\sigma(X) = -1$
A2: $\sigma(X) \in \mathbb{R}$
A3: $\sigma(X) > 0 $
A4: $ \sigma(X) = \sqrt{\mathrm{Var}(X) } $
Q2: Let $X$ be a continuous random variable where the distribution is given by the normal distribution. What is the correct pdf?
A1: $f_X(x) $ $ = \frac{1}{\sigma \sqrt{2 \pi} } \exp\Big( - \frac{1}{2} \frac{(x- \mu)^2}{\sigma^2} \Big) $
A2: $f_X(x) $ $ = \frac{1}{\sigma \sqrt{\pi} } \log \Big( - \frac{1}{2} \frac{(x- \mu)^2}{\sigma^2} \Big) $
A3: $f_X(x) $ $ = - \frac{1}{\sigma \sqrt{2 \pi} } \exp\Big( \frac{1}{2} \frac{(x- \mu)^2}{\sigma^2} \Big) $
A4: $f_X(t) $ $ = \int_0^t \frac{1}{\sigma \sqrt{\pi} } \log \Big( - \frac{1}{2} \frac{(x- \mu)^2}{\sigma^2} \Big) dx $
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Last update: 2025-09
